In this paper, we prove that the five-dimensional Schwarzschild- Tangherlini solution of the Einstein vacuum equations is orbitally stable (in the fully non-linear theory) with respect to vacuum perturbations of initial data preserving triaxial Bianchi-IX symmetry. More generally, we prove that five-dimensional vacuum spacetimes developing from suitable asymptotically flat triaxial Bianchi-IX symmetric initial data and containing a trapped or marginally trapped homogeneous 3-surface necessarily possess a complete null infinity I+, whose past J-(I+) is bounded to the future by a regular event horizon H+, whose cross-sectional volume in turn satisfies a Penrose inequality, relating it to the final Bondi mass. In particular, the results of this paper give the first examples of vacuum black holes which are not stationary exact solutions.
|Original language||English (US)|
|Number of pages||21|
|Journal||Advances in Theoretical and Mathematical Physics|
|State||Published - Aug 2006|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)